数学分解因式之十字相乘法和分组分解法要过程

分组分解法a^2-4b^2+12bc-9c^2
=a²-(2b-3c)²
=(a+2b-3c)(a-2b+3c)
十字相乘法1).4x^2+30x+14
=2(2x²+15x+7)
=2(2x+1)(x+7)
2).3x^2-8x+4
=(3x-2)(x-2)
3).5x^2y^2+23xy-10
=(5xy-2)(xy-5)
4).4x^2y^2-5x y^2-9y^2
=y²(4x²-5x-9)
=y²(4x-9)(x+1)
分组分解法1).x^2-xy+3y-3x
=x(x-y)-3(x-y)
=(x-y)(x-3)
2)9x^2+6x+1-3(3x+1)
=(3x+1)²-3(3x+1)
=(3x+1)(3x+1-3)
=(3x+1)(3x-2)
3).a^2+2ab+b^2-x^2-2xy-y^2
=(a+b)²-(x+y)²
=(a+b+x+y)(a+b-x-y)
4).2y^2-5xy+2x^2-ax+2ay
=(2x-y)(x-2y) -a(x-2y)
=(x-2y)(2x-y-a)
已知x+y=0.5,x+3y=1.2,求3x^2+12xy+9y^2
原式=3(x²+4xy+3y²)
=3(x+y)(x+3y)
=3×0.5×1.2
=1.8
已知xy=-5,a-b=6,求a^2xy+b^2xy-2abxy
原式=xy(a²-2ab+b²)
=xy(a-b)²
=-5×6²
=-180